Problems from the discrete to the continuous: probability, number theory, graph theory, and combinatorics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2014
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIII, 154 S. |
| ISBN: | 9783319079646 |
Internformat
MARC
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| 100 | 1 | |a Pinsky, Ross G. |d 1955- |e Verfasser |0 (DE-588)141663146 |4 aut | |
| 245 | 1 | 0 | |a Problems from the discrete to the continuous |b probability, number theory, graph theory, and combinatorics |c Ross G. Pinsky |
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2014 | |
| 300 | |a XIII, 154 S. | ||
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| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027568230 | ||
Datensatz im Suchindex
| _version_ | 1804152606849761280 |
|---|---|
| adam_text | Contents
1
Partitions
with Restricted Summands
or the Money Changing Problem
...................................... 1
2
The Asymptotic Density of Relatively Prime Pairs and
of Square-Free Numbers
................................................... 7
3
A One-Dimensional Probabilistic Packing Problem
.................... 21
4
The
A resine
Laws for the One-Dimensional Simple
Symmetric Random Walk
................................................. 35
5
The Distribution of Cycles in Random Permutations
.................. 49
6
Cheby
shev s Theorem on the Asymptotic Density of the Primes
...... 67
7
Mertens Theorems on the Asymptotic Behavior of the Primes
....... 75
8
The Hardy-Ramanujan Theorem on the Number
of Distinct Prime Divisors
................................................. 81
9
The Largest Clique in a Random Graph and Applications
to Tampering Detection and Ramsey Theory
............................ 89
9.1
Graphs and Random Graphs: Basic Definitions
.................... 89
9.2
The Size of the Largest Clique in a Random Graph
................ 91
9.3
Detecting Tampering in a Random Graph
.......................... 99
9.4
Ramsey Theory
....................................................... 104
10
The Phase Transition Concerning the Giant Component
in a Sparse Random Graph: A Theorem of
Erdős
and
Rényi
......... 109
10.1
Introduction and Statement of Results
.............................. 109
10.2
Construction of the Setup for the Proofs
ofTheorems
10.1
and
10.2...........................................
Ill
10.3
Some Basic Large Deviations Estimates
............................ 113
10.4
Proof of Theorem
10.1............................................... 115
Xl
xii Contents
10.5 The Galton-Watson
Branching Process
............................. 116
10.6
Proof of Theorem
10.2............................................... 120
Appendix A A Quick Primer on Discrete Probability
..................... 133
Appendix
В
Power Series and Generating Functions
..................... 141
Appendix
С
A Proof of Stirling s Formula
................................. 145
AppendixD An Elementary Proof of
Σ.Τ=ι^
=
Τ
......................
149
References
......................................................................... 151
Index
............................................................................... 153
Ross G. Pinsky
Problems from the Discrete to the Continuous
Probability, Number Theory, Graph Theory, and Combinatorics
The primary intent of the book is to introduce an array of beautiful problems in a
variety of subjects quickly, pithily and completely rigorously to graduate students
and advanced undergraduates. The book takes a number of specific problems
and solves them, the needed tools developed along the way in the context of the
particular problems. It treats
a mélange
of topics from combinatorial probability
theory, number theory, random graph theory and combinatorics. The problems in
this book involve the asymptotic analysis of a discrete construct as some natural
parameter of the system tends to infinity Besides bridging discrete mathematics and
mathematical analysis, the book makes a modest attempt at bridging disciplines.
The problems were selected with an eye toward accessibility to a wide audience,
including advanced undergraduate students. The book could be used for a seminar
course in which students present the lectures.
|
| any_adam_object | 1 |
| author | Pinsky, Ross G. 1955- |
| author_GND | (DE-588)141663146 |
| author_facet | Pinsky, Ross G. 1955- |
| author_role | aut |
| author_sort | Pinsky, Ross G. 1955- |
| author_variant | r g p rg rgp |
| building | Verbundindex |
| bvnumber | BV042128078 |
| classification_rvk | SK 110 SK 170 |
| ctrlnum | (OCoLC)900206573 (DE-599)BVBBV042128078 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042128078 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:13:23Z |
| institution | BVB |
| isbn | 9783319079646 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027568230 |
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| physical | XIII, 154 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Pinsky, Ross G. 1955- Verfasser (DE-588)141663146 aut Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics Ross G. Pinsky Cham [u.a.] Springer 2014 XIII, 154 S. txt rdacontent n rdamedia nc rdacarrier Universitext Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 s Zahlentheorie (DE-588)4067277-3 s Graphentheorie (DE-588)4113782-6 s Kombinatorik (DE-588)4031824-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-07965-3 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027568230&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027568230&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Pinsky, Ross G. 1955- Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd Graphentheorie (DE-588)4113782-6 gnd Zahlentheorie (DE-588)4067277-3 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4132446-8 (DE-588)4113782-6 (DE-588)4067277-3 (DE-588)4031824-2 |
| title | Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics |
| title_auth | Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics |
| title_exact_search | Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics |
| title_full | Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics Ross G. Pinsky |
| title_fullStr | Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics Ross G. Pinsky |
| title_full_unstemmed | Problems from the discrete to the continuous probability, number theory, graph theory, and combinatorics Ross G. Pinsky |
| title_short | Problems from the discrete to the continuous |
| title_sort | problems from the discrete to the continuous probability number theory graph theory and combinatorics |
| title_sub | probability, number theory, graph theory, and combinatorics |
| topic | Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd Graphentheorie (DE-588)4113782-6 gnd Zahlentheorie (DE-588)4067277-3 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Kombinatorische Wahrscheinlichkeitstheorie Graphentheorie Zahlentheorie Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027568230&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027568230&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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